Mathletics: How Gamblers, Managers, and Sports Enthusiasts Use Mathematics in Baseball, Basketball, and Football

We have all heard Marv Albert tell us that Dirk Nowitzki is “on fire” or
Jack Buck tell us that Albert Pujols is “red hot” and nobody can get him
out. We also hear announcers tell us the Spurs are on a hot streak, are unbeatable, and so forth. Is it true that athletes and teams encounter hot
streaks, or are the observed patterns of player and team performance just
randomness at work?

What Does a Random Sequence Look Like?

Let's first examine how a random sequence of 162 wins and losses appears.
Let's suppose a team wins 60% of their games. To generate a random sequence of 162 games, we should make sure that in each game the team has
a 0.60 chance of winning and that the chance of winning a game does not
depend on the team's recent history. For example, whether the team lost
their last five games or won their last five games, their chance of winning
the next game should still be 0.60. Figure 11.1 shows three randomly generated sequences of 162 games. In examining these data, most people
would think they are looking at a “streaky team,” even though these sequences were generated by assumptions that involve no streakiness.

These sequences were generated by essentially flipping a coin 162 times
with a 0.60 chance of a win. A 1 denotes a win and a 0 a loss. First note that
on average we would expect 162(.6) = 97.2 wins and in none of our random
sequences did this number of wins occur. This is because of the randomness
inherent in the coin- tossing pro cess. Also note that in each sequence the
team experiences several long winning streaks. For example, in the second
sequence the team had winning streaks of ten, nine, seven, and six games.
Most people think the occurrence of winning streaks indicates momentum or
a “hot team” effect, but here we see long winning streaks are simply random.

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